The rule with manifold is, no more than 2 surfaces can share the same edge. By having the corners touch, you end up having 4 walls sharing the same edge. You can move it out .00001 and it will work as it separates their edges. Then you'll just need to follow the individual materials rules for holes, wall thickness and separation.

I learned a long time ago the wisest thing I can do is be on my own side, be an advocate for myself and others like me. -Maya Angelou
michael@shapeways.com Community Advocate

When I visit the specs for Strong and Flexible Plastics, I see numbers for "Embossed Detail" and "Engraved Detail". This is neither of those things, I don't think. I also see "Accuracy" so maybe I should use that number?

For the accuracy, that means you could expect those sections to either be a little thicker, or a little thinner. I'm not seeing it on the page, but this should be considered a detail, which in the plastic materials you generally want to have at least 1:1 meaning a detail can have a wall under the minimum (.7mm for WSF) as long as it is no larger than it is thick. So say a tooth on a T-rex. If it's only .5mm thick, it can only be .5mm long. Your model should follow this, and also has the added benefit of not being free standing (as it is connected). So over all, I am 95% sure you'd be able to do this for WSF. To be a little extra certain, email you model to support, and they'll scan it over and tell you anything you may need to adjust.

I learned a long time ago the wisest thing I can do is be on my own side, be an advocate for myself and others like me. -Maya Angelou
michael@shapeways.com Community Advocate

I guess my question was two-part... 1. would my shape be rejected, and more importantly 2. would it be rejected for a good reason (i.e., it wouldn't print well). I can upload the shape to answer #1 but not #2.

I now understand that I can pass the manifold error check by separating or joining my holes by whatever minimal amount my software supports. (.01 mm I think, as I am in Tinkercad).

I HOPE your comment also implies that the printer won't have any problem creating these walls.